Different varieties of shapes differ indigenous each various other in regards to sides or angles. Plenty of shapes have actually 4 sides, but the difference in angle on their sides makes them unique. We speak to these 4-sided forms the quadrilaterals.

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**In this article, you will learn:**

## What is a Quadrilateral?

As words suggests, ‘**Quad**’ means four and also ‘**lateral**’ way side. Thus a square is a **closed two-dimensional polygon comprised of 4-line segments**. In an easy words, **a square is a form with four sides**.

Quadrilaterals space everywhere! from the books, chart papers, computer keys, television, and mobile screens. The perform of real-world instances of quadrilaterals is endless.

## Types that Quadrilaterals

There room **six quadrilaterals in geometry**. Several of the quadrilaterals space surely acquainted to you, if others may not be so familiar.

Let’s take it a look.

RectangleSquaresTrapeziumParallelogramRhombusKite** A rectangle **

A rectangle is a quadrilateral through 4 ideal angles (90°). In a rectangle, both the pairs of the contrary sides are parallel and equal in length.

**Properties that a rhombus**

## Properties of Quadrilaterals

*The nature of quadrilateral include:*

Sum of interior angles = 180 ° * (n – 2), whereby n is equal to the number of sides the the polygon

Rectangles, rhombus, and squares are all types of parallelograms.A square is both a rhombus and a rectangle.The rectangle and also rhombus space not square.A parallel is a trapezium.A trapezium is not a parallelogram.Kite is no a parallelogram.### Classification that quadrilaterals

*The quadrilaterals space classified right into two an easy types:*

There is another less common kind of quadrilaterals, called complicated quadrilaterals. These are crossed figures. Because that example, overcome trapezoid, overcome rectangle, overcome square, etc.

Let’s work-related on a few example problems around quadrilaterals.

*Example 1*

The interior angles of one irregular quadrilateral are; x°, 80°, 2x°, and also 70°. Calculate the value of x.

Solution

By a property of quadrilateral (Sum of internal angles = 360°), we have,

⇒ x° + 80° + 2x° + 70° =360°

Simplify.

⇒ 3x + 150° = 360°

Subtract 150° ~ above both sides.

⇒ 3x + 150° – 150° = 360° – 150°

⇒ 3x = 210°

Divide both sides by 3 to get;

⇒ x = 70°

Therefore, the value of x is 70°

And the angles of the quadrilaterals are; 70°, 80°, 140°, and 70°.

*Example 2*

The internal angles of a quadrilateral are; 82°, (25x – 2) °, (20x – 1) ° and (25x + 1) °. Uncover the angles of the quadrilateral.

Solution

The total sum of interior angles that in a quadrilateral = 360°

⇒ 82° + (25x – 2) ° + (20x – 1) ° + (25x + 1) ° = 360°

⇒ 82 + 25x – 2 + 20x – 1 + 25x + 1 = 360

Simplify.

⇒ 70x + 80 = 360

Subtract both sides by 80 to get;

⇒ 70x = 280

Divide both sides by 70.

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⇒ x = 4

By substitution,

⇒ (25x – 2) = 98°

⇒ (20x – 1) = 79°

⇒ (25x + 1) = 101°

Therefore, the angle of the square are; 82°, 98°, 79°, and 101°.

*Practice Questions*

Consider a parallelogram PQRS, whereFind the 4 internal angles of the rhombus whose sides and one of the diagonals space of equal length. *Practice Questions*

Answers